Interpolation on lattices generated by cubic pencils

: Principal lattices are distributions of points in the plane obtained from a triangle by drawing equidistant parallel lines to the sides and taking the intersection points as nodes. Interpolation on principal lattices leads to particularly simple formulae. These sets were generalized by Lee and Phillips considering three-pencil lattices, generated by three linear pencils. Inspired by the addition of points on cubic curves and using duality, we introduce an addition of lines as a way of constructing lattices generated by cubic pencils. They include three-pencil lattices and then principal lattices. Interpolation on lattices generated by cubic pencils has the same good properties and simple formulae as on principal lattices.

• Type: Journal
• Year: 2006
• Where: ADCM
• Authors: Jesús M. Carnicer, Mariano Gasca
• Keywords: ADCM 2006, Equidistant Parallel Lines, Principal Lattices, Three-pencil Lattices